// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_INVERSE_IMPL_H
#define EIGEN_INVERSE_IMPL_H

namespace Eigen {

namespace internal {

/**********************************
*** General case implementation ***
**********************************/

template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
struct compute_inverse
{
	EIGEN_DEVICE_FUNC
	static inline void run(const MatrixType& matrix, ResultType& result) { result = matrix.partialPivLu().inverse(); }
};

template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
struct compute_inverse_and_det_with_check
{ /* nothing! general case not supported. */
};

/****************************
*** Size 1 implementation ***
****************************/

template<typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 1>
{
	EIGEN_DEVICE_FUNC
	static inline void run(const MatrixType& matrix, ResultType& result)
	{
		typedef typename MatrixType::Scalar Scalar;
		internal::evaluator<MatrixType> matrixEval(matrix);
		result.coeffRef(0, 0) = Scalar(1) / matrixEval.coeff(0, 0);
	}
};

template<typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1>
{
	EIGEN_DEVICE_FUNC
	static inline void run(const MatrixType& matrix,
						   const typename MatrixType::RealScalar& absDeterminantThreshold,
						   ResultType& result,
						   typename ResultType::Scalar& determinant,
						   bool& invertible)
	{
		using std::abs;
		determinant = matrix.coeff(0, 0);
		invertible = abs(determinant) > absDeterminantThreshold;
		if (invertible)
			result.coeffRef(0, 0) = typename ResultType::Scalar(1) / determinant;
	}
};

/****************************
*** Size 2 implementation ***
****************************/

template<typename MatrixType, typename ResultType>
EIGEN_DEVICE_FUNC inline void
compute_inverse_size2_helper(const MatrixType& matrix, const typename ResultType::Scalar& invdet, ResultType& result)
{
	typename ResultType::Scalar temp = matrix.coeff(0, 0);
	result.coeffRef(0, 0) = matrix.coeff(1, 1) * invdet;
	result.coeffRef(1, 0) = -matrix.coeff(1, 0) * invdet;
	result.coeffRef(0, 1) = -matrix.coeff(0, 1) * invdet;
	result.coeffRef(1, 1) = temp * invdet;
}

template<typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 2>
{
	EIGEN_DEVICE_FUNC
	static inline void run(const MatrixType& matrix, ResultType& result)
	{
		typedef typename ResultType::Scalar Scalar;
		const Scalar invdet = typename MatrixType::Scalar(1) / matrix.determinant();
		compute_inverse_size2_helper(matrix, invdet, result);
	}
};

template<typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 2>
{
	EIGEN_DEVICE_FUNC
	static inline void run(const MatrixType& matrix,
						   const typename MatrixType::RealScalar& absDeterminantThreshold,
						   ResultType& inverse,
						   typename ResultType::Scalar& determinant,
						   bool& invertible)
	{
		using std::abs;
		typedef typename ResultType::Scalar Scalar;
		determinant = matrix.determinant();
		invertible = abs(determinant) > absDeterminantThreshold;
		if (!invertible)
			return;
		const Scalar invdet = Scalar(1) / determinant;
		compute_inverse_size2_helper(matrix, invdet, inverse);
	}
};

/****************************
*** Size 3 implementation ***
****************************/

template<typename MatrixType, int i, int j>
EIGEN_DEVICE_FUNC inline typename MatrixType::Scalar
cofactor_3x3(const MatrixType& m)
{
	enum
	{
		i1 = (i + 1) % 3,
		i2 = (i + 2) % 3,
		j1 = (j + 1) % 3,
		j2 = (j + 2) % 3
	};
	return m.coeff(i1, j1) * m.coeff(i2, j2) - m.coeff(i1, j2) * m.coeff(i2, j1);
}

template<typename MatrixType, typename ResultType>
EIGEN_DEVICE_FUNC inline void
compute_inverse_size3_helper(const MatrixType& matrix,
							 const typename ResultType::Scalar& invdet,
							 const Matrix<typename ResultType::Scalar, 3, 1>& cofactors_col0,
							 ResultType& result)
{
	// Compute cofactors in a way that avoids aliasing issues.
	typedef typename ResultType::Scalar Scalar;
	const Scalar c01 = cofactor_3x3<MatrixType, 0, 1>(matrix) * invdet;
	const Scalar c11 = cofactor_3x3<MatrixType, 1, 1>(matrix) * invdet;
	const Scalar c02 = cofactor_3x3<MatrixType, 0, 2>(matrix) * invdet;
	result.coeffRef(1, 2) = cofactor_3x3<MatrixType, 2, 1>(matrix) * invdet;
	result.coeffRef(2, 1) = cofactor_3x3<MatrixType, 1, 2>(matrix) * invdet;
	result.coeffRef(2, 2) = cofactor_3x3<MatrixType, 2, 2>(matrix) * invdet;
	result.coeffRef(1, 0) = c01;
	result.coeffRef(1, 1) = c11;
	result.coeffRef(2, 0) = c02;
	result.row(0) = cofactors_col0 * invdet;
}

template<typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 3>
{
	EIGEN_DEVICE_FUNC
	static inline void run(const MatrixType& matrix, ResultType& result)
	{
		typedef typename ResultType::Scalar Scalar;
		Matrix<typename MatrixType::Scalar, 3, 1> cofactors_col0;
		cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType, 0, 0>(matrix);
		cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType, 1, 0>(matrix);
		cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType, 2, 0>(matrix);
		const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
		const Scalar invdet = Scalar(1) / det;
		compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
	}
};

template<typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
{
	EIGEN_DEVICE_FUNC
	static inline void run(const MatrixType& matrix,
						   const typename MatrixType::RealScalar& absDeterminantThreshold,
						   ResultType& inverse,
						   typename ResultType::Scalar& determinant,
						   bool& invertible)
	{
		typedef typename ResultType::Scalar Scalar;
		Matrix<Scalar, 3, 1> cofactors_col0;
		cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType, 0, 0>(matrix);
		cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType, 1, 0>(matrix);
		cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType, 2, 0>(matrix);
		determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
		invertible = Eigen::numext::abs(determinant) > absDeterminantThreshold;
		if (!invertible)
			return;
		const Scalar invdet = Scalar(1) / determinant;
		compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);
	}
};

/****************************
*** Size 4 implementation ***
****************************/

template<typename Derived>
EIGEN_DEVICE_FUNC inline const typename Derived::Scalar
general_det3_helper(const MatrixBase<Derived>& matrix, int i1, int i2, int i3, int j1, int j2, int j3)
{
	return matrix.coeff(i1, j1) *
		   (matrix.coeff(i2, j2) * matrix.coeff(i3, j3) - matrix.coeff(i2, j3) * matrix.coeff(i3, j2));
}

template<typename MatrixType, int i, int j>
EIGEN_DEVICE_FUNC inline typename MatrixType::Scalar
cofactor_4x4(const MatrixType& matrix)
{
	enum
	{
		i1 = (i + 1) % 4,
		i2 = (i + 2) % 4,
		i3 = (i + 3) % 4,
		j1 = (j + 1) % 4,
		j2 = (j + 2) % 4,
		j3 = (j + 3) % 4
	};
	return general_det3_helper(matrix, i1, i2, i3, j1, j2, j3) + general_det3_helper(matrix, i2, i3, i1, j1, j2, j3) +
		   general_det3_helper(matrix, i3, i1, i2, j1, j2, j3);
}

template<int Arch, typename Scalar, typename MatrixType, typename ResultType>
struct compute_inverse_size4
{
	EIGEN_DEVICE_FUNC
	static void run(const MatrixType& matrix, ResultType& result)
	{
		result.coeffRef(0, 0) = cofactor_4x4<MatrixType, 0, 0>(matrix);
		result.coeffRef(1, 0) = -cofactor_4x4<MatrixType, 0, 1>(matrix);
		result.coeffRef(2, 0) = cofactor_4x4<MatrixType, 0, 2>(matrix);
		result.coeffRef(3, 0) = -cofactor_4x4<MatrixType, 0, 3>(matrix);
		result.coeffRef(0, 2) = cofactor_4x4<MatrixType, 2, 0>(matrix);
		result.coeffRef(1, 2) = -cofactor_4x4<MatrixType, 2, 1>(matrix);
		result.coeffRef(2, 2) = cofactor_4x4<MatrixType, 2, 2>(matrix);
		result.coeffRef(3, 2) = -cofactor_4x4<MatrixType, 2, 3>(matrix);
		result.coeffRef(0, 1) = -cofactor_4x4<MatrixType, 1, 0>(matrix);
		result.coeffRef(1, 1) = cofactor_4x4<MatrixType, 1, 1>(matrix);
		result.coeffRef(2, 1) = -cofactor_4x4<MatrixType, 1, 2>(matrix);
		result.coeffRef(3, 1) = cofactor_4x4<MatrixType, 1, 3>(matrix);
		result.coeffRef(0, 3) = -cofactor_4x4<MatrixType, 3, 0>(matrix);
		result.coeffRef(1, 3) = cofactor_4x4<MatrixType, 3, 1>(matrix);
		result.coeffRef(2, 3) = -cofactor_4x4<MatrixType, 3, 2>(matrix);
		result.coeffRef(3, 3) = cofactor_4x4<MatrixType, 3, 3>(matrix);
		result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum();
	}
};

template<typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 4>
	: compute_inverse_size4<Architecture::Target, typename MatrixType::Scalar, MatrixType, ResultType>
{};

template<typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
{
	EIGEN_DEVICE_FUNC
	static inline void run(const MatrixType& matrix,
						   const typename MatrixType::RealScalar& absDeterminantThreshold,
						   ResultType& inverse,
						   typename ResultType::Scalar& determinant,
						   bool& invertible)
	{
		using std::abs;
		determinant = matrix.determinant();
		invertible = abs(determinant) > absDeterminantThreshold;
		if (invertible && extract_data(matrix) != extract_data(inverse)) {
			compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
		} else if (invertible) {
			MatrixType matrix_t = matrix;
			compute_inverse<MatrixType, ResultType>::run(matrix_t, inverse);
		}
	}
};

/*************************
*** MatrixBase methods ***
*************************/

} // end namespace internal

namespace internal {

// Specialization for "dense = dense_xpr.inverse()"
template<typename DstXprType, typename XprType>
struct Assignment<DstXprType,
				  Inverse<XprType>,
				  internal::assign_op<typename DstXprType::Scalar, typename XprType::Scalar>,
				  Dense2Dense>
{
	typedef Inverse<XprType> SrcXprType;
	EIGEN_DEVICE_FUNC
	static void run(DstXprType& dst,
					const SrcXprType& src,
					const internal::assign_op<typename DstXprType::Scalar, typename XprType::Scalar>&)
	{
		Index dstRows = src.rows();
		Index dstCols = src.cols();
		if ((dst.rows() != dstRows) || (dst.cols() != dstCols))
			dst.resize(dstRows, dstCols);

		const int Size = EIGEN_PLAIN_ENUM_MIN(XprType::ColsAtCompileTime, DstXprType::ColsAtCompileTime);
		EIGEN_ONLY_USED_FOR_DEBUG(Size);
		eigen_assert(((Size <= 1) || (Size > 4) || (extract_data(src.nestedExpression()) != extract_data(dst))) &&
					 "Aliasing problem detected in inverse(), you need to do inverse().eval() here.");

		typedef typename internal::nested_eval<XprType, XprType::ColsAtCompileTime>::type ActualXprType;
		typedef typename internal::remove_all<ActualXprType>::type ActualXprTypeCleanded;

		ActualXprType actual_xpr(src.nestedExpression());

		compute_inverse<ActualXprTypeCleanded, DstXprType>::run(actual_xpr, dst);
	}
};

} // end namespace internal

/** \lu_module
 *
 * \returns the matrix inverse of this matrix.
 *
 * For small fixed sizes up to 4x4, this method uses cofactors.
 * In the general case, this method uses class PartialPivLU.
 *
 * \note This matrix must be invertible, otherwise the result is undefined. If you need an
 * invertibility check, do the following:
 * \li for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
 * \li for the general case, use class FullPivLU.
 *
 * Example: \include MatrixBase_inverse.cpp
 * Output: \verbinclude MatrixBase_inverse.out
 *
 * \sa computeInverseAndDetWithCheck()
 */
template<typename Derived>
EIGEN_DEVICE_FUNC inline const Inverse<Derived>
MatrixBase<Derived>::inverse() const
{
	EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger, THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
	eigen_assert(rows() == cols());
	return Inverse<Derived>(derived());
}

/** \lu_module
 *
 * Computation of matrix inverse and determinant, with invertibility check.
 *
 * This is only for fixed-size square matrices of size up to 4x4.
 *
 * Notice that it will trigger a copy of input matrix when trying to do the inverse in place.
 *
 * \param inverse Reference to the matrix in which to store the inverse.
 * \param determinant Reference to the variable in which to store the determinant.
 * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
 * \param absDeterminantThreshold Optional parameter controlling the invertibility check.
 *                                The matrix will be declared invertible if the absolute value of its
 *                                determinant is greater than this threshold.
 *
 * Example: \include MatrixBase_computeInverseAndDetWithCheck.cpp
 * Output: \verbinclude MatrixBase_computeInverseAndDetWithCheck.out
 *
 * \sa inverse(), computeInverseWithCheck()
 */
template<typename Derived>
template<typename ResultType>
inline void
MatrixBase<Derived>::computeInverseAndDetWithCheck(ResultType& inverse,
												   typename ResultType::Scalar& determinant,
												   bool& invertible,
												   const RealScalar& absDeterminantThreshold) const
{
	// i'd love to put some static assertions there, but SFINAE means that they have no effect...
	eigen_assert(rows() == cols());
	// for 2x2, it's worth giving a chance to avoid evaluating.
	// for larger sizes, evaluating has negligible cost and limits code size.
	typedef typename internal::conditional<
		RowsAtCompileTime == 2,
		typename internal::remove_all<typename internal::nested_eval<Derived, 2>::type>::type,
		PlainObject>::type MatrixType;
	internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run(
		derived(), absDeterminantThreshold, inverse, determinant, invertible);
}

/** \lu_module
 *
 * Computation of matrix inverse, with invertibility check.
 *
 * This is only for fixed-size square matrices of size up to 4x4.
 *
 * Notice that it will trigger a copy of input matrix when trying to do the inverse in place.
 *
 * \param inverse Reference to the matrix in which to store the inverse.
 * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
 * \param absDeterminantThreshold Optional parameter controlling the invertibility check.
 *                                The matrix will be declared invertible if the absolute value of its
 *                                determinant is greater than this threshold.
 *
 * Example: \include MatrixBase_computeInverseWithCheck.cpp
 * Output: \verbinclude MatrixBase_computeInverseWithCheck.out
 *
 * \sa inverse(), computeInverseAndDetWithCheck()
 */
template<typename Derived>
template<typename ResultType>
inline void
MatrixBase<Derived>::computeInverseWithCheck(ResultType& inverse,
											 bool& invertible,
											 const RealScalar& absDeterminantThreshold) const
{
	Scalar determinant;
	// i'd love to put some static assertions there, but SFINAE means that they have no effect...
	eigen_assert(rows() == cols());
	computeInverseAndDetWithCheck(inverse, determinant, invertible, absDeterminantThreshold);
}

} // end namespace Eigen

#endif // EIGEN_INVERSE_IMPL_H
